He said: "We have to end this unfair farce whereby middle class parents dominate the best schools, when they could afford to pay, and even boast of their moral superiority in using the state system when all they are doing is squeezing out the poor from the best schools."

He said they should be liable for the fees if they had a combined household income of £80,000 a year or more.

Dr Seldon, headmaster of £11,000-a-term Wellington College in Berkshire, also said private schools should set aside a quarter of places for poorer pupils.

In a report to be published by the Social Market Foundation think tank on Wednesday, he said the money could be used to pay for more teachers and smaller classes.

His suggested starting point for fees – £80,000 – is the average income of the top 10 per cent of the population, but 'the more the parents earn, the more they should pay'.

Families earning more than £200,000 a year with children at the most over-subscribed state schools would pay the most – up to £20,000 a year for a secondary place and £15,000 for a primary place, equivalent to the fees of a private school.

Dr Seldon said: "Grammar schools, popular academies and comprehensives would be the most expensive schools."

Just three per cent of pupils at the country's 166 grammar schools come from the poorest homes.

Dr Seldon added it was only fair that if parents could afford to pay for better schooling – secured by buying houses in the right catchment areas or paying for private tutors to help their children pass grammar school entry exams – they should be made to do so.

He said: "Instead of estate agents and private tutors getting rich, let's put this money into the state system."